A Trefftz/MFS mixed-type method to solve the Cauchy problem of the Laplace equation

被引：4

作者：

Liu, Chein-Shan ^{[1
,2
]}

Wang, Fajie ^{[3
]}

Gu, Yan ^{[4
]}

机构：

[1] Hohai Univ, Coll Mech & Mat, Ctr Numer Simulat Software Engn & Sci, Nanjing 210098, Jiangsu, Peoples R China

[2] Natl Taiwan Ocean Univ, Ctr Excellence Ocean Engn, Dept Mech & Mechatron Engn, Keelung 20224, Taiwan

[3] Qingdao Univ, Sch Electromech Engn, Qingdao 266071, Peoples R China

[4] Qingdao Univ, Coll Math, Qingdao 266071, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 87卷

关键词：

Laplace equation; Cauchy problem; Trefftz method; MFS test functions; Mixed-type method; BOUNDARY-ELEMENT METHOD; REGULARIZATION METHOD;

D O I：

10.1016/j.aml.2018.07.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By using the multiple-scale Trefftz method (MSTM) to solve the Cauchy problem of the Laplace equation in an arbitrary bounded domain, we may lose the accuracy several orders when the noise being imposed on the specified Cauchy data is quite large. In addition to the linear equations obtained from the MSTM, the fundamental solutions play as the test functions being inserted into a derived boundary integral equation. Therefore, after merely supplementing a few linear equations in the mixed-type method (MTM), which is a well organized combination of the Trefftz method and the method of fundamental solutions (MFS), we can improve the ill-conditioned behavior of the linear equations system and hence increase the accuracy of the solution for the Cauchy problem significantly, as explored by two numerical examples. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：87 / 92

页数：6

共 50 条

[21] A first order method for the Cauchy problem for the Laplace equation using BEM
Delvare, Franck
Cimetiere, Alain
COMPUTATIONAL MECHANICS, 2008, 41 (06) : 789 - 796
[22] A first order method for the Cauchy problem for the Laplace equation using BEM
Franck Delvare
Alain Cimetiere
Computational Mechanics, 2008, 41 : 789 - 796
[23] Wavelets and regularization of the Cauchy problem for the Laplace equation
Qiu, Chun-Yu
Fu, Chu-Li
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) : 1440 - 1447
[24] Regularization of the Cauchy problem for the Laplace equation
V. V. Tikhomirov
N. N. Ochilov
Differential Equations, 2014, 50 : 1128 - 1132
[25] Method of fundamental solutions for a Cauchy problem of the Laplace equation in a half-plane
Chen, Bo
Sun, Yao
Zhuang, Zibo
BOUNDARY VALUE PROBLEMS, 2019, 2019 (1)
[26] Applications of the modified Trefftz method for the Laplace equation
Chen, Yung-Wei
Liu, Chein-Shan
Chang, Jiang-Ren
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2009, 33 (02) : 137 - 146
[27] Method of fundamental solutions for a Cauchy problem of the Laplace equation in a half-plane
Bo Chen
Yao Sun
Zibo Zhuang
Boundary Value Problems, 2019
[28] An order optimal regularization method for the Cauchy problem of a Laplace equation in an annulus domain
He, Dongdong
Pan, Kejia
APPLIED MATHEMATICAL MODELLING, 2015, 39 (10-11) : 3063 - 3074
[29] Regularization of the Cauchy problem for the Laplace equation
Tikhomirov, V. V.
Ochilov, N. N.
DIFFERENTIAL EQUATIONS, 2014, 50 (08) : 1128 - 1132
[30] An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant
Chapko, Roman
Johansson, B. Tomas
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2009, 17 (07) : 871 - 883

← 1 2 3 4 5 →